ISO/TR 3313:2018

TECHNICAL ISO/TR
REPORT 3313
Fourth edition
2018-03
Measurement of fluid flow in closed
conduits — Guidelines on the effects of
flow pulsations on flow-measurement
instruments
Mesurage du débit des fluides dans les conduites fermées — Lignes
directrices relatives aux effets des pulsations d'écoulement sur les
instruments de mesure de débit
Reference number
ISO/TR 3313:2018(E)
©
ISO 2018

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ISO/TR 3313:2018(E)

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© ISO 2018
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ISO/TR 3313:2018(E)

Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols and subscripts . 2
5 Description and detection of pulsating flow. 4
5.1 Nature of pipe flows . 4
5.2 Threshold between steady and pulsating flow . 4
5.2.1 General. 4
5.2.2 Differential pressure (DP) type flowmeters . 5
5.2.3 Turbine flowmeters . 5
5.2.4 Vortex flowmeters . 6
5.3 Causes of pulsation . 6
5.4 Occurrence of pulsating flow conditions in industrial and laboratory
flowmeter installations . 6
5.5 Detection of pulsation and determination of frequency, amplitude and waveform . 7
5.5.1 General. 7
5.5.2 Characteristics of the ideal pulsation sensor . 7
5.5.3 Non-intrusive techniques . 7
5.5.4 Insertion devices . 8
5.5.5 Signal analysis on existing flowmeter outputs: software tools. 8
6 Measurement of the mean flowrate of a pulsating flow.10
6.1 Orifice plate, nozzle, and Venturi tube .10
6.1.1 Description of pulsation effects and parameters .10
6.1.2 Flowmeters using slow-response DP sensors .12
6.1.3 Flowmeters using fast-response DP sensors .14
6.1.4 Pulsation damping.15
6.2 Turbine flowmeters .20
6.2.1 Description of pulsation effects and parameters .20
6.2.2 Estimation of pulsation correction factors and measurement uncertainties .23
6.3 Vortex flowmeters .24
6.3.1 Pulsation effects .24
6.3.2 Minimizing pulsation effects .25
6.3.3 Estimation of measurement uncertainties .25
Annex A (informative) Orifice plates, nozzles and Venturi tubes — Theoretical considerations .27
Annex B (informative) Orifice plates, nozzles and Venturi tubes — Pulsation damping criteria .34
Annex C (informative) Turbine flowmeters — Theoretical background and experimental data .40
Bibliography .44
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ISO/TR 3313:2018(E)

Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see the following
URL: www .iso .org/ iso/ foreword .html
This document was prepared by Technical Committee ISO/TC 30, Measurement of fluid flow in closed
conduits, Subcommittee SC 2, Pressure differential devices.
This fourth edition of ISO/TR 3313:2018 is a technical revision of ISO/TR 3313:1998, which was
withdrawn in 2013.
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TECHNICAL REPORT ISO/TR 3313:2018(E)
Measurement of fluid flow in closed conduits — Guidelines
on the effects of flow pulsations on flow-measurement
instruments
1 Scope
This document defines pulsating flow, compares it with steady flow, indicates how it can be detected,
and describes the effects it has on orifice plates, nozzles or Venturi tubes, turbine and vortex flowmeters
when these devices are being used to measure fluid flow in a pipe. These particular flowmeter types
feature in this document because they are amongst those types most susceptible to pulsation effects.
Methods for correcting the flowmeter output signal for errors produced by these effects are described
for those flowmeter types for which this is possible. When correction is not possible, measures to avoid
or reduce the problem are indicated. Such measures include the installation of pulsation damping
devices and/or choice of a flowmeter type which is less susceptible to pulsation effects.
This document applies to flow in which the pulsations are generated at a single source which is situated
either upstream or downstream of the primary element of the flowmeter. Its applicability is restricted
to conditions where the flow direction does not reverse in the measuring section but there is no
restriction on the waveform of the flow pulsation. The recommendations within this document apply
to both liquid and gas flows although with the latter the validity might be restricted to gas flows in
which the density changes in the measuring section are small as indicated for the particular type of
flowmeter under discussion.
2 Normative references
There are no normative references in this document.
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.1
steady flow
flow in which parameters such as velocity, pressure, density and temperature do not vary significantly
enough with time to prevent measurement to within the required uncertainty of measurement
3.2
pulsating flow
flow in which the flowrate in a measuring section is a function of time but has a constant mean value
when averaged over a sufficiently long period of time, which depends on the regularity of the pulsation
Note 1 to entry: Pulsating flow can be divided into two categories:
— periodic pulsating flow;
— randomly fluctuating flow.
Note 2 to entry: For further amplification of what constitutes steady or pulsating flow see 5.1 and 5.2.
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ISO/TR 3313:2018(E)

Note 3 to entry: Unless otherwise stated in this document the term “pulsating flow” is always used to describe
periodic pulsating flow.
4 Symbols and subscripts
4.1 Symbols
A area
A area of the throat of a Venturi nozzle
d
A turbine blade aspect ratio
R
th
a , b , c amplitude of the r harmonic component in the undamped or damped pulsation
r r r
B bf /q , dimensionless dynamic response parameter
p V
b turbine flowmeter dynamic response parameter
C turbine blade chord length
C contraction coefficient
c
C discharge coefficient
D
C velocity coefficient
v
c speed of sound
D internal diameter of the tube
d throat bore of orifice, nozzle or Venturi tube
E
R residual error in time-mean flowrate when calculated using the quantity Δp
E total error in the time-mean flowrate
T
f turbine flowmeter output signal, proportional to volumetric flowrate
f pulsation frequency
p
f resonant frequency
r
f vortex-shedding frequency
v
H harmonic distortion factor
Ho Hodgson number
I moment of inertia
I , I moments of inertia of turbine rotor and fluid contained in rotor envelope respectively
R F
k/D relative roughness of pipe wall
L turbine blade length
L effective axial length
e
l impulse line length for differential pressure (DP) measurement device
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2
m = β orifice or nozzle throat to pipe area ratio
N number of blades on turbine rotor
p pressure (absolute)
q mass flowrate
m
q volume flowrate
V
R turbine blade mean radius
Re Reynolds number
r , r turbine blade hub and tip radii respectively
h t
Sr Strouhal number
Sr Strouhal number based on orifice diameter
d
t time
t turbine blade thickness
b
U axial bulk-mean velocity
U bulk-mean velocity based on orifice diameter
d
V volume
X temporal inertia term for short pulsation wavelengths
α
′
UU/
RMS
β orifice or nozzle throat to pipe diameter ratio
γ ratio of specific heat capacities (c /c )
p V
Δp differential pressure
Δϖ pressure loss
ε expansibility factor for steady flow conditions
ss
η blade “airfoil efficiency”
θ phase angle
κ isentropic exponent (= γ for a perfect gas)
μ damping response factor (see 6.1.4.1.3)
ρ fluid density
ρ turbine blade material density
b
τ = p /p pressure ratio
2 1
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maximum allowable uncertainty in the indicated flowrate due to pulsation at the
φ
flowmeter
ψ maximum allowable relative error
ω = 2πf angular pulsation frequency
p
4.2 Subscripts and superscripts
o pulsation source
p measured under pulsating flow conditions, possibly damped
po measured under pulsating flow conditions before damping
RMS root mean square
ss measured under steady flow conditions
(over-bar) the time-mean value
1,2 measuring sections
'
fluctuating component about mean value, e.g. U′
5 Description and detection of pulsating flow
5.1 Nature of pipe flows
Truly steady pipe flow is only found in laminar flow conditions which can normally only exist when
the pipe Reynolds number, Re, is below about 2 000. Most industrial pipe flows have higher Reynolds
numbers and are turbulent which means that they are only statistically steady. Such flows contain
continual irregular and random fluctuations in quantities such as velocity, pressure and temperature.
Nevertheless, if the conditions are similar to those which are typical of fully developed turbulent pipe
flow and there is no periodic pulsation, the provisions of such standards as ISO 5167 (all parts) apply.
The magnitude of the turbulent fluctuations increases with pipe roughness, and this is one of the
reasons why ISO 5167 (all parts) stipulates a maximum allowable relative roughness, k/D, of the
upstream pipe for each type of primary device covered by ISO 5167 (all parts).
ISO 5167 (all parts), however, cannot be applied to flows which contain any periodic flow variation or
pulsation.
5.2 Threshold between steady and pulsating flow
5.2.1 General
If the amplitude of the periodic flowrate variations is sufficiently small there should not be any error
in the indicated flowrate greater than the normal measurement uncertainty. It is possible to define
amplitude thresholds for both differential pressure (DP) type flowmeters and turbine flowmeters
without reference to pulsation frequency. It is also possible to do this for vortex flowmeters but extreme
caution is necessary if even the smallest amplitude is known to be present in the flow.
For DP-type flowmeters, the threshold is relevant when slow-response DP cells are being used. In the
case of turbine flowmeters, the threshold value is relevant when there is any doubt about the ability
of the rotor to respond to the periodic velocity fluctuations. In the case of a vortex flowmeter the
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pulsation frequency relative to the vortex-shedding frequency is a much more important parameter
than the velocity pulsation amplitude.
5.2.2 Differential pressure (DP) type flowmeters
The threshold can be defined in terms of the velocity pulsation amplitude such that the flow can be
treated as steady if
′
U
RMS
≤00, 5 (1)
U
where U is the instantaneous bulk-mean axial velocity such that
′
UU= +U (2)
where
is the periodic velocity fluctuation;
U′
is the time-mean value.
U
The threshold in terms of the equivalent DP pulsation amplitude is
Δp′
pR, MS
≤01, 0 (3)
Δp
p
where Δp is the instantaneous differential pressure across the tappings of the primary device such that
p
′
ΔΔpp=Δ + p (4)
p p p
where
is the time-mean value;
Δp
p
is the periodic differential pressure fluctuation.
′
Δp
p
To determine the velocity pulsation amplitude it is necessary to use one of the techniques described
in 5.5 such as laser Doppler or thermal anemometry. To determine the DP pulsation amplitude it is
necessary to use a fast-response DP sensor and to observe the rules governing the design of the
complete secondary instrumentation system as described in 6.1.3.
Theoretical considerations are covered in Annex A.
5.2.3 Turbine flowmeters
At a given velocity pulsation amplitude a turbine flowmeter tends to read high as the frequency of
pulsation increases and exceeds the frequency at which the turbine rotor can respond faithfully to the
velocity fluctuations. The positive systematic error reaches a plateau value depending on the amplitude
and thus the threshold amplitude can be defined such that the resulting maximum systematic error is
still within the general measurement uncertainty. For example, if the overall measurement uncertainty
is greater than or equal to 0,5 % then it can be assumed that a systematic error due to pulsation of
0,1 % or less has negligible effect on the overall measurement uncertainty.
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′
The velocity amplitude of sinusoidal pulsation, UU/ , that produces a systematic error of 0,1 % in a
RMS
turbine flowmeter is 3,5 %. Thus the threshold for sinusoidal pulsation is given by
U′
RMS
≤0,035 (5)
U
Techniques such as laser Doppler and thermal anemometry can be used to determine the velocity
pulsation amplitude. If the flowmeter output is a pulse train at the blade passing frequency and if the
rotor inertia is known, then signal analysis can be used to determine the flow pulsation amplitude as
described in 6.2.
5.2.4 Vortex flowmeters
A vortex flowmeter is subject to very large pulsation errors when the vortex-shedding process locks
in to the flow pulsation. There is a danger of this happening when the pulsation frequency is near the
vortex-shedding frequency. At a sufficiently low amplitude, locking-in does not occur and flow-metering
errors due to pulsation are negligible. This threshold amplitude, however, is only about 3 % of the mean
velocity and is comparable to the velocity turbulence amplitude. The consequences of not detecting the
pulsation or erroneously assuming the amplitude is below the threshold can be very serious. This issue
is discussed further in 6.3.
5.3 Causes of pulsation
Pulsation occurs commonly in industrial pipe flows. It might be generated by rotary or reciprocating
positive displacement engines, compressors, blowers and pumps. Rotodynamic machines might also
induce small pulsation at blade passing frequencies. Pulsation can also be produced by positive-
displacement flowmeters. Vibration, particularly at resonance, of pipe runs and flow control equipment
is also a potential source of flow pulsation, as are periodic actions of flow controllers, e.g. valve
“hunting” and governor oscillations. Pulsation might also be generated by flow separation within pipe
fittings, valves, or rotary machines (e.g. compressor surge).
Flow pulsation can also be due to hydrodynamic oscillations generated by geometrical features of
the flow system and multiphase flows (e.g. slugging). Vortex shedding from bluff bodies such as
thermometer wells, or trash grids, or vortex-shedding flowmeters fall into this category. Self-excited
flow oscillations at tee-branch connections are another example.
5.4 Occurrence of pulsating flow conditions in industrial and laboratory flowmeter
installations
In industrial flows, there is often no obvious indication of the presence of pulsation, and the associated
errors, because of the slow-response times and heavy damping of the pressure and flow instrumentation
commonly used. Whenever factors such as those indicated in 5.3 are present, there is the possibility of
flow pulsation occurring. It should also be appreciated that pulsation can travel upstream as well as
downstream and thus possible pulsation sources could be on either side of the flowmeter installation.
However, amplitudes might be small and, depending on the distance from pulsation source to
flowmeter, might be attenuated by compressibility effects (in both liquids and gases) to undetectable
levels at the flowmeter location. Pulsation frequencies range from fractions of a hertz to a few hundred
hertz; pulsation amplitudes relative to mean flow vary from a few percent to 100 % or larger. At low
percentage amplitudes the question arises of discrimination between pulsation and turbulence.
Flow pulsation can be expected to occur in various situations in petrochemical and process industries,
natural gas distribution flows at end-user locations and internal combustion engine flow systems. Flow-
metering calibration systems might also experience pulsation arising from, for example, rotodynamic
pump blade passing effects and the effects of rotary positive-displacement flowmeters.
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5.5 Detection of pulsation and determination of frequency, amplitude and waveform
5.5.1 General
If the presence of pulsation is suspected then there are various techniques available to determine the
flow pulsation characteristics.
5.5.2 Characteristics of the ideal pulsation sensor
The ideal sensor would be non-intrusive, would measure mass flowrate, or bulk flow velocity, and
would have a bandwidth from decihertz to several kilohertz. The sensor would respond to both liquids
and gases and not require any supplementary flow seeding. The technique would not require optical
transparency or constant fluid temperature. The sensor would be uninfluenced by pipe wall material,
transparency or thickness. The device would have no moving parts, its response would be linear, its
calibration reliable and unaffected by changes in ambient temperature.
5.5.3 Non-intrusive techniques
5.5.3.1 Optical: laser Doppler anemometry (LDA)
This technology is readily available, but expensive. Measurement of point velocity on the tube axis allows
an estimate only of bulk flow pulsation amplitude and waveform but, for constant frequency pulsation,
accurate frequency measurements can be made. Optical access to an optically transparent fluid is
either by provision of a transparent tube section, or insertion of a probe with fibre-optic coupling. With
the exception of detecting low frequency pulsation, supplementary seeding of the flow would probably
be required to produce an adequate bandwidth. LDA characteristics are comprehensively described in
Reference [2].
5.5.3.2 Acoustic: Doppler shift; transit time
Non-intrusive acoustic techniques are suitable for liquid flows only, because for gas flows there is
poor acoustic-impedance match between the pipe wall and flowing gases. For the externally mounted
transmitter and receiver, usually close-coupled to the tube wall, an acoustically transparent signal path
is essential. The Doppler shift technique might require flow seeding to provide adequate scattering.
Instruments for point velocity measurements are available which, as for the LDA, provide only an
estimate of bulk flow pulsation amplitude and waveform. Moreover, Doppler-derived “instantaneous”
[3]
full-velocity profile instruments allow much closer estimates of bulk flow pulsation characteristics.
Transit-time instruments measure an average velocity, most commonly along a diagonal path across
the flow. All acoustic techniques are limited in bandwidth by the requirement that reflections from one
pulse of ultrasound should decay before transmission of the next pulse. Many commercial instruments
do not provide the signal processing required to resolve unsteady flow components. An investigation
[4]
by Hakansson on a transit time, intrusive-type ultrasonic flowmeter for gases subjected to pulsating
flows showed that only small shifts in the calibration took place and that these were attributable to the
changing velocity profile.
5.5.3.3 Electromagnetic flowmeters
When the existing flowmeter installation is an electromagnetic device, then, if it is of the pulsed d.c. field
type (likely maximum d.c. pulse frequency a few hundred hertz), there is the capability to resolve flow
pulsation up to frequencies approximately five times below the excitation frequency. This technique
is only suitable for liquids with an adequate electrical conductivity. It provides a measure of bulk flow
[5]
pulsation, although there is some dependence upon velocity profile shape .
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5.5.4 Insertion devices
5.5.4.1 Thermal anemometry
The probes used measure point velocity, and relatively rugged (e.g. fibre-film) sensors are available for
industrial flows. These probes generally have an adequate bandwidth, but the amplitude response is
inherently non-linear. As with other point velocity techniques, pulsation amplitude and waveform can
only be estimated. Estimates of pulsation velocity amplitude relative to mean velocity may be made
without calibration. The RMS value of the fluctuating velocity component can be determined by using
a true RMS flowmeter to measure the fluctuating component of the linearized anemometer output
voltage. Mean-sensing RMS flowmeters should not be used as these only read correctly for sinusoidal
waveforms. Accurate frequency measurements from spectral analysis can be made for constant
frequency pulsation.
Applications are limited to clean, relatively cool, non-flammable and non-hostile fluids. Cleanness of flow
is very important; even nominally clean flows can result in rapid fouling of probes with a consequent
dramatic loss of response. A constant temperature flow is desirable although a slowly varying fluid
temperature can be accommodated.
5.5.4.2 Other techniques
Insertion versions of both acoustic and electromagnetic flowmeters are available. Transit-time acoustic
measurements can be made in gas flows when the transmitter and receiver are directly coupled to the
[6]
flow , although this might require a permanent insertion. Again there is the limitation of a lack of
commercially available instrumentation with the necessary signal processing to resolve time-varying
velocity components.
Insertion electromagnetic flowmeters are not widely available and are subject to the same bandwidth
limitations as the tube version, due to the maximum sampling frequency of the signal.
5.5.5 Signal analysis on existing flowmeter outputs: software tools
5.5.5.1 Orifice plate with fast-response DP sensor
A fast-response secondary measurement system is capable of correctly following the time-varying
pressure difference produced by the primary instrument provided the rules given in 6.1.3.2 can be
followed. In principle, a numerical solution of the pressure difference/flow relationship derived from
the quasi-steady temporal inertia model, Formula (A.11), would then provide an approximation to
the instantaneous flow. The square-root error would not be present, although other measurement
uncertainties (e.g. C variations, compressibility effects) produced by the pulsation would be. Successive
D
numerical solutions would then provide an approximation to the flow as a function of time and, hence,
amplitude and waveform information. Fr
...